Surface area

Learning Objectives Define surface area and identify the components of 3D shapes (faces, bases, lateral area). Calculate the surface area of right prisms and cylinders using the correct formulas. Calculate the surface area of right pyramids and cones, including finding the slant height when necessary. Calculate the surface area of a sphere. Solve multi-step problems involving the surface area of composite 3D objects. Algebraically rearrange surface area formulas to solve for an unknown dimension, such as radius or height. Ever wondered how much wrapping paper you *actually* need for a gift, or how much paint to buy for your room? 🎁 That's all about surface area! In this tutorial, we'll explore surface area, which is the total area of all the outside surfaces of a...

TermDefinitionExample Surface Area (SA)The sum of the areas of all the faces or surfaces of a three-dimensional object. It is measured in square units (e.g., cm², m²).The surface area of a cube with 2 cm sides is the sum of the areas of its 6 square faces: 6 * (2 cm * 2 cm) = 24 cm². NetA two-dimensional pattern that can be folded to create a three-dimensional shape.A T-shape made of six squares is a net for a cube. Calculating the area of the net gives you the surface area of the cube. Lateral AreaThe surface area of a 3D object, excluding the area of its base(s).For a can of soup, the lateral area is the paper label that wraps around the can, not including the top and bottom metal circles. BaseThe face of a 3D object from which its height is measured. Prisms and cylinders have two paral...

Surface Area of a Right Cylinder SA = 2πr² + 2πrh Use this for any right cylinder, like a can or a pipe. '2πr²' is the area of the two circular bases, and '2πrh' is the lateral area (the rectangle that wraps around). Surface Area of a Right Cone SA = πr² + πrl Use this for any right cone. 'πr²' is the area of the circular base, and 'πrl' is the lateral area. 'l' is the slant height, not the perpendicular height. Surface Area of a Sphere SA = 4πr² Use this for any sphere, like a ball or a globe. This formula calculates the entire outer surface area. Surface Area of a Right Pyramid SA = (Area of Base) + (Area of all triangular faces) This is a general rule. For a square-based pyramid, it becomes SA = s² + 2sl, w...